Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C3×C5×C4⋊C4 ⋊ C2 |
| Hall | C3×C5 ⋊ #117 |
| Sylow | C5 ⋊ #892 |
| Sylow | C3 ⋊ #4038 |
152 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2,4,5,3)(6,7,8)(9,10,11,12)(14,18)(15,19);(13,15,16,19)(14,17,18,20);(2,3)(4,5)(7,8)(13,14)(15,17)(16,18)(19,20)Polycyclic presentation:
2^5,3,5|b^2=e,c^2=d,c^a=ce,f^a=f^2,g^a=g^4,c^b=ce90 conjugacy classes — view the full character table.
| maximal subgroup of | #11747334, #11747335, #11747336, … |
| maximal normal subgroup of | #11747334, #11747335, #11747336, … |
| maximal quotient of | #11750749, #11750752, #11750756, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 857);